TY - JOUR

T1 - Reasoning about distributed information with infinitely many agents

AU - Guzmán, Michell

AU - Knight, Sophia

AU - Quintero, Santiago

AU - Ramírez, Sergio

AU - Rueda, Camilo

AU - Valencia, Frank

N1 - Publisher Copyright:
© 2021 Elsevier Inc.

PY - 2021/6

Y1 - 2021/6

N2 - Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. For completely distributive lattices, we establish that the distributed information of c amongst a group is the greatest lower bound of all possible combinations of information in the spaces of the agents in the group that derive c. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide an application to mathematical morphology where dilations, one of its fundamental operations, define an scs on a powerset lattice. We show that distributed information represents a particular dilation in such scs.

AB - Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. For completely distributive lattices, we establish that the distributed information of c amongst a group is the greatest lower bound of all possible combinations of information in the spaces of the agents in the group that derive c. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide an application to mathematical morphology where dilations, one of its fundamental operations, define an scs on a powerset lattice. We show that distributed information represents a particular dilation in such scs.

KW - Algebraic modeling

KW - Distributed knowledge

KW - Infinitely many agents

KW - Mathematical morphology

KW - Reasoning about groups

KW - Reasoning about space

UR - http://www.scopus.com/inward/record.url?scp=85103326894&partnerID=8YFLogxK

U2 - 10.1016/j.jlamp.2021.100674

DO - 10.1016/j.jlamp.2021.100674

M3 - Article

AN - SCOPUS:85103326894

SN - 2352-2208

VL - 121

JO - Journal of Logical and Algebraic Methods in Programming

JF - Journal of Logical and Algebraic Methods in Programming

M1 - 100674

ER -